Theorem snexg

Description: A singleton built on a set is a set. Special case of snex which is intuitionistically valid. (Contributed by NM, 7-Aug-1994) (Revised by Mario Carneiro, 19-May-2013) Extract from snex and shorten proof. (Revised by BJ, 15-Jan-2025) (Proof shortened by GG, 6-Mar-2026)

	Ref	Expression
Assertion	snexg	⊢ ( 𝐴 ∈ 𝑉 → { 𝐴 } ∈ V )

Proof

Step	Hyp	Ref	Expression
1		snex	⊢ { 𝐴 } ∈ V
2	1	a1i	⊢ ( 𝐴 ∈ 𝑉 → { 𝐴 } ∈ V )